Regular PapersNo Access

AN INVESTIGATION OF UNIFORM EXPANSIONS OF LARGE ORDER BESSEL FUNCTIONS IN GRAVITATIONAL WAVE SIGNALS

F. A. CHISHTIE

Department of Applied Mathematics, University of Western Ontario, London, Canada

Search for more papers by this author

K. M. RAO

Department of Physics, University of Toronto, Toronto, Canada

Search for more papers by this author

I. S. KOTSIREAS

Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Canada

Search for more papers by this author

, and

S. R. VALLURI

Department of Physics and Astronomy and Department of Applied Mathematics, University of Western Ontario, London, Canada

Search for more papers by this author

https://doi.org/10.1142/S0218271808012760Cited by:4 (Source: Crossref)

Abstract

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, particularly the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, global parameter space correlations of a coherent matched filtering search for continuous GWs from isolated neutron stars and tomographic reconstruction of GW LISA sources. The uniform expansion we consider here is found to be valid in the entire range of the argument.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

K. Jotania, S. R. Valluri and S. V. Dhurandhar, Astron. Astrophys. 306, 317 (1996). Web of Science, ADS, Google Scholar
S. R. Valluri, F. A. Chishtie et al., Class. Quant. Grav. 19 (2002) 1327. Erratum, ibid. 19 (2002) 4227 . Google Scholar
S. R. Valluri, F. A. Chishtie and A. Vajda, Class. Quant. Grav. 23, 3323 (2006), DOI: 10.1088/0264-9381/23/10/005. Crossref, Web of Science, ADS, Google Scholar
R. H. MacPhie and K. L. Wu, IEEE Trans. Antennas Propagation 51, 2801 (2003), DOI: 10.1109/TAP.2003.818009. Crossref, Web of Science, Google Scholar
K. S. Thorne, Rev. Mod. Phys. 52, 299 (1980), DOI: 10.1103/RevModPhys.52.299. Crossref, Web of Science, ADS, Google Scholar
B. Allen and A. C. Ottewill, Phys. Rev. D 56, 54563 (1997), DOI: 10.1103/PhysRevD.56.545. Google Scholar
G. N. Watson , A Treatise on the Theory of Bessel Functions ( Cambridge University Press , 1958 ) . Google Scholar
D. F. E. Meissel, Astr. Nach. CXXIX, 281 (1892). Google Scholar
D. F. E. Meissel, Astr. Nach. CXXX, 363 (1892). Google Scholar
D. F. E. Meissel, Astr. Nach. CXXVII, 359 (1891). Google Scholar
D. F. E. Meissel, Astr. Nach. CXXVIII, 145 (1891). Google Scholar
F. A. Chishtie et al. , Proc. 19th Annual Symposium on High Performance Computing Systems & Applications (HPCS 2005) ( IEEE Computer Society Press , Guelph, Ontario, Canada ) . Google Scholar
M. Abramowitz and I. A. Stegun , Handbook of Mathematical Functions ( National Bureau of Standards , 1964 ) . Google Scholar
M. E. Normandin, A. Vajda and S. R. Valluri, Matched filtering a gravitational wave pulsar signal involving reciprocal gamma functions, Proc. 2007 International Workshop on Symbolic-Numeric Computation, eds. J. Verschelde and S. M. Watt (Association for Computing Machinery, 2007) pp. 133–141. Google Scholar
R. Prix and Y. Itoh, Class. Quant. Grav. 22, S1003 (2005), DOI: 10.1088/0264-9381/22/18/S14. Crossref, Web of Science, Google Scholar
P. C. Peters and J. Mathews, Phys. Rev. 131, 435 (1963), DOI: 10.1103/PhysRev.131.435. Crossref, Web of Science, ADS, Google Scholar
L. Barack and C. Cutler, Phys. Rev. D 69, 082005 (2004), DOI: 10.1103/PhysRevD.69.082005. Crossref, Web of Science, Google Scholar
V. Pierroet al., Mon. Not. R. Astron. Soc. 325, 358 (2001), DOI: 10.1046/j.1365-8711.2001.04442.x. Crossref, Web of Science, ADS, Google Scholar
S. D. Mohanty and R. K. Nayak, Phys. Rev. D 73, 083006 (2006), DOI: 10.1103/PhysRevD.73.083006. Crossref, Web of Science, Google Scholar
M. V. Berry and K. E. Mount, Rep. Progr. Phys. 35, 315 (1972), DOI: 10.1088/0034-4885/35/1/306. Crossref, Web of Science, ADS, Google Scholar
K. W. Ford and J. A. Wheeler, Ann. Phys. 7, 259 (1959). Crossref, Web of Science, ADS, Google Scholar
W. J. Romo and S. R. Valluri, Physica Scripta 71, 1 (2005), DOI: 10.1088/0031-8949/71/6/002. Google Scholar
T. Regge and J. A. Wheeler, Phys. Rev. 108, 1063 (1957), DOI: 10.1103/PhysRev.108.1063. Crossref, Web of Science, Google Scholar
T. Poston and I. Stewart , Catastrophe Theory and Its Applications ( Pitman , London , 1978 ) . Google Scholar
M. V. Berry, J. Phys. A 8, 566 (1975), DOI: 10.1088/0305-4470/8/4/019. Crossref, ADS, Google Scholar
N. M. Temme, Numerical Algorithms 15, 207 (1997), DOI: 10.1023/A:1019197921337. Crossref, Web of Science, ADS, Google Scholar
P. Debye, Math. Ann. LXVII, 535 (1909). Google Scholar
J. R. Airy, Philos. Mag. XXXI(6), 520 (1916). Google Scholar
D. Baruth, Bessel functions of large orders and arguments, www.iging.com/transcendental/J_1000000.htm . Google Scholar
J.-P. Allouche and J. Shallit, Theor. Comput. Sci. 98, 163 (1992), DOI: 10.1016/0304-3975(92)90001-V. Crossref, Web of Science, Google Scholar
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, www.research.att.com/~njas/sequences . Google Scholar
D. E. Amos, ACM Trans. Math. Software 12, 265 (1986), DOI: 10.1145/7921.214331. Crossref, Web of Science, Google Scholar